
Here we consider the dissipation tensors, \( \Pi ^{\mu \nu } \)  and \( \tilde{\Pi }^{\mu \nu } \) , to be symmetric, transverse and traceless i.e., \( {g}_{\mu \nu }\Pi ^{\mu \nu } = 0 \)  and \({\tilde{g}}_{\mu \nu }\tilde{\Pi }^{\mu \nu } \) . These conditions imply that there is only one independent component of \( \Pi ^{\mu \nu } \)  for each sector, which we call \( \Pi ^\eta _{\,\,\eta } = -\phi \)  (the longitudinal non-equilibrium pressure) following the convention in [1]}, which means that
\(\Pi ^{\mu \nu } &= \text{diag}\left(0,\frac{\phi (\tau )}{2},\frac{\phi (\tau )}{2},\frac{-\phi (\tau )}{\tau ^2}\right) ,\\\tilde{ \Pi }^{\mu \nu } &= \text{diag}\left(0,\frac{\tilde{\phi }(\tau )}{2},\frac{\tilde{\phi }(\tau )}{2},\frac{-\tilde{\phi }(\tau )}{\tau ^2}\right).\) 
